The performance of tracking signals and control charts in process monitoring

In the field of statistical process control, the Individuals, Cumulative Sum and Exponentially Weighted Moving Average control charts have traditionally been used to monitor production processes. In the forecasting and time series fields, the Cumulative Sum and Smoothed Error tracking signals perform a similar function, the monitoring of forecasting systems. These monitoring schemes are compared in their ability to detect step shifts in the level of an autocorrelated process. Forecast errors from simple exponential smoothing are investigated. The criteria used are Average Run Lengths and Cumulative Distribution Functions (CDFs) of the run lengths. The CDF provides a method for comparing monitoring schemes based on the probability of early detection of step shifts. Based on the CDF criterion, the Individuals chart offers the greatest probability of detecting step changes in the mean of a time series early, regardless of the size of the step increase.